Mathematics ยท Quantitative Aptitude

Geometry of Triangles and Angles

758 Questions

Triangle and angle geometry covers angle sums, properties of equilateral shapes, and right triangles. These principles form the basis of advanced quantitative aptitude sections. Practicing spatial problems helps secure points in exams.

Triangle angle sumsPythagorean theoremProperties of equilateral trianglesComplementary and supplementary anglesRight triangle formulas

Geometry of Triangles and Angles Questions

Multiple choice

In a triangle, if two sides and the included angle are congruent to the corresponding sides and included angle of another triangle, then the triangles are:

  1. Congruent

  2. Similar

  3. Isosceles

  4. Scalene
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

By the Side-Angle-Side (SAS) congruence theorem, if two sides and the included angle of one triangle are congruent to the corresponding sides and included angle of another triangle, then the triangles are congruent.

Multiple choice

In a triangle, if two angles and the included side are congruent to the corresponding angles and included side of another triangle, then the triangles are:

  1. Congruent

  2. Similar

  3. Isosceles

  4. Scalene
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

By the Angle-Side-Angle (ASA) congruence theorem, if two angles and the included side of one triangle are congruent to the corresponding angles and included side of another triangle, then the triangles are congruent.

Multiple choice

In a triangle, if three sides are congruent to the corresponding sides of another triangle, then the triangles are:

  1. Congruent

  2. Similar

  3. Isosceles

  4. Scalene
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

By the Side-Side-Side (SSS) congruence theorem, if three sides of one triangle are congruent to the corresponding sides of another triangle, then the triangles are congruent.

Multiple choice

Two triangles are congruent if they have:

  1. Congruent sides and angles

  2. Similar sides and angles

  3. Equal areas

  4. All of the above
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Two triangles are congruent if they have congruent sides and angles, similar sides and angles, or equal areas.

Multiple choice

If two triangles are congruent, then their corresponding:

  1. Sides are congruent

  2. Angles are congruent

  3. Areas are congruent

  4. All of the above
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

If two triangles are congruent, then their corresponding sides, angles, and areas are all congruent.

Multiple choice

In a right triangle, if the hypotenuse and one leg are congruent to the hypotenuse and one leg of another right triangle, then the triangles are:

  1. Congruent

  2. Similar

  3. Isosceles

  4. Scalene
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

By the Hypotenuse-Leg (HL) congruence theorem, if the hypotenuse and one leg of one right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

Multiple choice

In a triangle, if two sides are congruent and the third side is not congruent, then the triangle is:

  1. Congruent

  2. Similar

  3. Isosceles

  4. Scalene
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A triangle with two congruent sides and one non-congruent side is called an isosceles triangle.

Multiple choice

In a triangle, if all three sides are congruent, then the triangle is:

  1. Congruent

  2. Similar

  3. Equilateral

  4. Scalene
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A triangle with all three sides congruent is called an equilateral triangle.

Multiple choice

Two triangles are similar if they have:

  1. Congruent sides and angles

  2. Similar sides and angles

  3. Equal areas

  4. None of the above
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Two triangles are similar if they have similar sides and angles, but not necessarily congruent sides and angles.

Multiple choice

If two triangles are similar, then their corresponding:

  1. Sides are proportional

  2. Angles are congruent

  3. Areas are proportional

  4. All of the above
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

If two triangles are similar, then their corresponding sides are proportional, their corresponding angles are congruent, and their corresponding areas are proportional.

Multiple choice

In a right triangle, if the hypotenuse is congruent to the hypotenuse of another right triangle, then the triangles are:

  1. Congruent

  2. Similar

  3. Isosceles

  4. Scalene
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

By the Hypotenuse-Hypotenuse (HH) similarity theorem, if the hypotenuse of one right triangle is congruent to the hypotenuse of another right triangle, then the triangles are similar.

Multiple choice

In a triangle, if two angles are congruent and the third angle is not congruent, then the triangle is:

  1. Congruent

  2. Similar

  3. Isosceles

  4. Scalene
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A triangle with two congruent angles and one non-congruent angle is called an isosceles triangle.

Multiple choice

In a triangle, if one angle is 90 degrees, then the triangle is:

  1. Congruent

  2. Similar

  3. Right

  4. Scalene
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A triangle with one angle measuring 90 degrees is called a right triangle.

Multiple choice

In a triangle, if the sum of the squares of two sides is equal to the square of the third side, then the triangle is:

  1. Congruent

  2. Similar

  3. Right

  4. Scalene
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

By the Pythagorean theorem, in a right triangle, the sum of the squares of the two shorter sides (legs) is equal to the square of the longest side (hypotenuse).

Multiple choice

In a triangle, if the square of one side is equal to the sum of the squares of the other two sides, then the triangle is:

  1. Congruent

  2. Similar

  3. Right

  4. Scalene
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

By the converse of the Pythagorean theorem, if the square of one side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.